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Having considered operations with decimals and fractions, we now consider operations that involve both decimals and fractions.
Perform the following operations.
$0\text{.}\text{38}\cdot \frac{1}{4}$ . Convert both numbers to decimals or both numbers to fractions. We’ll convert to decimals.
$\begin{array}{c}\hfill .25\\ \hfill 4\overline{)1.00}\\ \hfill \underline{8}\\ \hfill 20\\ \hfill \underline{20}\\ \hfill 0\end{array}$
To convert
$\frac{1}{4}$ to a decimal, divide 1 by 4.
Now multiply 0.38 and .25.
$\begin{array}{c}\hfill \stackrel{1}{\stackrel{4}{.3}}8\\ \hfill \underline{\times .25}\\ \hfill 190\\ \hfill \underline{76\text{}}\\ \hfill .0950\end{array}$
Thus, $0\text{.}\text{38}\cdot \frac{1}{4}=0\text{.}\text{095}$ .
In the problems that follow, the conversions from fraction to decimal, or decimal to fraction, and some of the additions, subtraction, multiplications, and divisions will be left to you.
$1\text{.}\text{85}+\frac{3}{8}\cdot 4\text{.}1$ Convert $\frac{3}{8}$ to a decimal.
$1\text{.}\text{85}+0\text{.}\text{375}\cdot 4\text{.}1$ Multiply before adding.
$1\text{.}\text{85}+1\text{.}\text{5375}$ Now add.
3.3875
$\frac{5}{\text{13}}\left(\frac{4}{5}-0\text{.}\text{28}\right)$ Convert 0.28 to a fraction.
$\begin{array}{ccc}\frac{5}{\text{13}}\left(\frac{4}{5}-\frac{\text{28}}{\text{100}}\right)& =& \frac{5}{\text{13}}\left(\frac{4}{5}-\frac{7}{\text{25}}\right)\hfill \\ & =& \frac{5}{\text{13}}\left(\frac{\text{20}}{\text{25}}-\frac{7}{\text{25}}\right)\hfill \\ & =& \frac{\stackrel{1}{\overline{)5}}}{\underset{1}{\overline{)13}}}\cdot \frac{\stackrel{1}{\overline{)13}}}{\underset{5}{\overline{)25}}}\hfill \\ & =& \frac{1}{5}\hfill \end{array}$
$\begin{array}{cccc}\frac{0.125}{1\frac{1}{3}}+\frac{1}{16}-0.1211& =& \frac{\frac{125}{1000}}{\frac{4}{3}}+\frac{1}{16}-0.1211\hfill & \\ & =& \frac{\frac{1}{8}}{\frac{4}{3}}+\frac{1}{16}-0.1211\hfill & \\ & =& \frac{1}{8}\cdot \frac{3}{4}+\frac{1}{16}-0.1211\hfill & \\ & =& \frac{3}{32}+\frac{1}{16}-0.1211\hfill & \\ & =& \frac{3}{32}+\frac{2}{32}-0.1211=\frac{5}{32}-0.1211\hfill & \\ & =& 0.15625-0.1211\hfill & \\ & =& 0.03515\hfill & \text{Convert this to fraction form}\hfill \\ & =& \frac{3515}{\mathrm{100,000}}\hfill & \\ & =& \frac{703}{\mathrm{20,000}}\hfill & \end{array}$
Perform the following operations.
$1\frac{9}{\text{16}}\left(6\text{.}\text{12}+\frac{7}{\text{25}}\right)$
10
$\frac{0\text{.}\text{156}}{1\frac{\text{11}}{\text{15}}}-0\text{.}\text{05}$
$\frac{1}{\text{25}}\text{or}0\text{.}\text{04}$
$\frac{1}{5}+0\text{.}1$
$0\text{.}\text{418}-\frac{\text{67}}{\text{200}}$
$\frac{3}{5}\cdot 8\text{.}4$
$\frac{3}{\text{20}}\xf70\text{.}\text{05}$
$1\frac{1}{\text{15}}\xf70\text{.}9\cdot 0\text{.}\text{12}$
$9\text{.}\text{26}+\frac{1}{4}\cdot 0\text{.}\text{81}$
9.4625
$0\text{.}\text{588}+\frac{1}{\text{40}}\cdot 0\text{.}\text{24}$
$\frac{1}{\text{20}}+3\text{.}\text{62}\cdot \frac{3}{8}$
1.4075
$7+0\text{.}\text{15}\xf7\frac{3}{\text{30}}$
$\frac{\text{15}}{\text{16}}\cdot \left(\frac{7}{\text{10}}-0\text{.}5\right)$
0.1875
$0\text{.}2\cdot \left(\frac{7}{\text{20}}+1\text{.}\text{1143}\right)$
$\frac{3}{4}\cdot \left(0\text{.}\text{875}+\frac{1}{8}\right)$
0.75
$5\text{.}\text{198}-0\text{.}\text{26}\cdot \left(\frac{\text{14}}{\text{250}}+0\text{.}\text{119}\right)$
${\left(1\text{.}4\right)}^{2}-1\text{.}6\frac{1}{2}$
${\left(\frac{3}{8}\right)}^{2}-0\text{.}\text{000625}+(1\text{.}1{)}^{2}$
1.35
${\left(0\text{.}6\right)}^{2}\cdot \left(\frac{1}{\text{20}}-\frac{1}{\text{25}}\right)$
$\frac{0\text{.}\text{75}}{4\frac{1}{2}}+\frac{5}{\text{12}}$
$\left(\frac{0\text{.}\text{375}}{2\frac{1}{\text{16}}}-\frac{1}{\text{33}}\right)$
$0\text{.}\overline{\text{15}}$
$8\frac{1}{3}\cdot \left(\frac{1\frac{1}{4}}{2\text{.}\text{25}}+\frac{9}{\text{25}}\right)$
$\frac{\frac{0\text{.}\text{32}}{\frac{\text{12}}{\text{35}}}}{0\text{.}\text{35}}$
$2\text{.}\overline{6}$
$\frac{\left(\sqrt{\frac{49}{64}}-5\right)0.125}{1.375}$
( [link] ) Expand ${14}^{4}$ . Do not find the actual value.
( [link] ) Find the prime factorization of 15,400.
${2}^{3}\cdot {5}^{2}\cdot 7\cdot 11$
( [link] ) Convert 8.016 to a fraction.
( [link] ) Find the quotient. $\text{16}\xf7\text{27}$ .
$0\text{.}\overline{\text{592}}$
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